537 


ENGINEERING 
LIBRARY 


U.S.  National  Bureau 
of  Standards 


THE  RELATION  OF  THE  HORSEPOWER 
TO  THE  KILOWATT 


THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

LOS  ANGELES 

GIFT  OF 

Dean  L.  M.  K.   Boelter 


DEPARTMENT   OF   COMMERCE 


CIRCULAR 

OF  THE 

BUREAU  OF  STANDARDS 


S.  W.  STRATTON,  DIRECTOR 


No.  34 


THE  RELATION  OF  THE  HORSEPOWER 
TO  THE  KILOWATT 


I3d  Edition] 
Issued  May  15.  1915 


WASHINGTON 
8OVIRNMENT  PRINTING  OFFICE 

1915 


CIRCULARS  ISSUED   BY  THE  BUREAU  OF  STANDARDS;  DEPART- 
MENT  OF  COMMERCE. 

1.  Verification  of  Standards  and  Measuring  Instruments. 

2.  Measurements  of  Length  and  Area,  Including  Thermal  Expansion* 

3.  Verification  of  Standards  of  Mass. 

4.  Verification  of  Standards  of  Capacity. 

5.  Testing  of  Clinical  Thermometers. 

6.  Fees  for  Electric,  Magnetic,  and  Photometric  Testing. 

7.  Pyrometer  Testing  and  Heat  Measurements. 

8.  Testing  of  Thermometers. 

9.  Testing  of  Glass  Volumetric  Apparatus. 

10.  Legal  Weights  (in  pounds)  per  Bushel  of  Various  Commodities. 

11.  The  Standardization  of  Bomb  Calorimeters. 

12.  Verification  of  Polariscopic  Apparatus. 

13.  United  States  Government  Standard  Specifications  for  Incandescent  Electric  Lamps. 

14.  Samples  of  Analyzed  Irons  and  Steels— Methods  of  Analysis. 

15.  A  Proposed  International  Unit  of  Light. 

16.  The  Testing  of  Hydrometers. 

17.  Magnetic  Testing. 

18.  Standard  Gauge  for  Sheet  and  Plate  Iron  and  Steel. 

19.  Standard  Density  and  Volumetric  Tables. 

20.  Electrical  Measuring  Instruments. 

21.  Precision  Measurements  of  Resistance  and  Electromotive  Force. 

22.  Standard  Specifications  for  Transformers,  Oil-immersed,  Self -cooled*  60-cyde,  220©  Volts. 

23.  Standardization  of  Electrical  Practice  in  Mines. 

24.  Publications  of  the  Bureau  of  Standards. 

25.  Standard  Analyzed  Samples — General  Information. 

26.  Analyzed  Iron  and  Manganese  Ores — Methods  of  Analysis. 

27.  The  Testing  and  Properties  of  Optical  Instruments. 

28.  The  Determination  of  the  Optical  Properties  of  Materials. 

29    Announcement  of  a  Change  in  the  Value  of  the  International  Volt. 

30.  Lime:  Its  Properties  and  Uses. 

31.  Copper  Wire  Tables. 

32.  Standard  Regulations  for  Manufactured  Gas  and  Gas  Service. 

33.  United  States  Government  Specifications  for  Portland  Cement. 

34.  The  Relation  of  the  Horsepower  to  the  Kilowatt. 

35.  Melting  Points  of  Chemical  Elements. 

36.  The  Testing  and  Properties  of  Electrical  Condensers. 

37.  Electric  Wire  and  Cable  Terminology. 

'38.  The  Physical  Testing  of  Mechanical  Rubber  Goods. 

39.  Specifications  for  and  Measurement  of  Standard  Sieves. 

40.  Sodium  Oxalate  as  a  Standard  in  Volumetric  Analysis. 

41.  Testing  and  Properties  of  Textile  Materials. 

42.  Metallographic  Testing. 

43.  The  Metric  Carat. 

44.  Polarimetry. 

45.  The  Testing  of  Materials. 

46.  Testing  of  Barometers. 

47.  Units  of  Weight  and  Measure;  Definitions  and  Tables  of  Equivalents. 

48.  Standards  of  Gas  Service. 

49.  Safety  Rules  to  be  Observed  in  the  Operation  and  Maintenance  of  Electrical  Equipment 

and  Line. 

50.  National  Standard  Hose  Couplings  and  Fittings  for  Public  Fire  Sendee. 

51.  Measurement  of  Time  and  Tests  of  Timepieces. 

52.  Regulation  of  Electrotyping  Solutions. 

53.  Composition,  Properties,  and  Testing  of  Printing  Inks, 

54.  Proposed  National  Electrical  Safety  Code. 


DEPARTMENT   OF   COMMERCE 


CIRCULAR 

OF  THE 

BUREAU  OF  STANDARDS 


S.  W.  STRATTON,  DIRECTOR 


No.  34 


THE  RELATION  OF  THE  HORSEPOWER 
TO  THE  KILOWATT 


[3d  Edition] 
Issued  May  15.  1915 


WASHINGTON 

GOVERNMENT  PRINTING  OFFICE 
1915 


ADDITIONAL  COPIES 

OP  THIS  PUBLICATION  MAT  BE  PKOCtTBED  FROM 

THE  SUPERINTENDENT  OF  DOCUMENTS 

GOVERNMENT  PRINTING  OFFICE 

WASHINGTON,  D.  C. 

AT 

5  CENTS  PER  COPY 


Engineering 


THE  RELATION  OF  THE  HORSEPOWER  TO  THE  KILOWATT 


The  horsepower  is  taken  by  the  Bureau  to  be  746  watts.  This  equiv- 
alent is  also  accepted  by  the  American  Institute  of  Electrical  Engineers, 
and  is  the  same  value  which  was  recommended  by  the  British  Association 
Committee  on  Units  in  1873.  This  equivalent  has  been  used  extensively 
in  practice,  but,  on  the  other  hand,  it  has  also  been  common  to  consider 
the  horsepower  as  equal  to  a  definite  number  of  foot-pounds  per  second, 
in  which  case  the  number  of  watts  equal  to  a  horsepower  varied  with  the 
value  of  the  acceleration  of  gravity.  It  is  desirable,  both  on  theoretical 
and  practical  grounds,  that  the  horsepower  represent  an  absolute  and  in- 
variable amount  of  power,  and  to  do  so  it  must  equal  a  definite  number  of 
watts.  So  defined,  its  equivalent  in  local  foot-pounds  per  second  varies 
with  latitude  and  altitude  in  a  determinate  manner.  The  definition  of 
the  pound  as  a  unit  of  force  is  intimately  involved,  and  it  is,  accordingly, 
treated  in  the  following  pages.  The  horsepower  defined  as  746  watts  is 
equivalent  to  550  foot-pounds  per  second  at  50°  latitude,  very  near  where 
the  original  experiments  were  made  by  James  Watt  to  establish  the  value 
of  the  horsepower. 

The  "continental  horsepower,"  which  is  used  in  Germany  and  France 
and  generally  on  the  continent  of  Europe,  is  equal  to  736  watts,  or  75 
kilogram-meters  per  second  at  Berlin.  It  is  thus  more  than  i  per  cent 
different  from  the  horsepower  as  used  in  the  United  States  and  Great 
Britain. 

Modern  practice  is  tending  toward  the  more  general  use  of  the  kilowatt 
and  the  disuse  of  the  horsepower.  This  practice  is  recommended  by  the 
Bureau. 

The  second  edition  (Aug.  i,  1914)  of  this  circular  differed  from  the 
first  (June  i,  1912)  in  the  addition  of  sections  treating  the  definition  of 
the  pound  as  a  unit  of  force  and  giving  standard  data  on  the  acceleration 
of  gravity.  The  values  used  for  gravity  supersede  those  used  in  the  first 
edition  and  also  the  value  used  in  this  Bureau's  "Tables  of  Equivalents." 
In  the  present  (third)  edition  only  minor  corrections  and  changes  have  been 
made. 

S.  W.  STRATTON, 

Director. 


I.  INTRODUCTION 

The  value  of  the  "  horsepower  "  may  be  expressed  either  in  gravitational 
or  in  absolute  units  of  power.  Confusion  often  results  when  one  equivalent 
is  reduced  to  the  other,  since  the  gravitational  units  depend  on  the  force  of 
gravity,  which  varies  from  place  to  place,  and  the  absolute  units  do  not. 
Thus,  the  usual  gravitational  value  for  the  English  horsepower,  550  foot- 
pounds per  second,  when  reduced  to  watts  gives  a  different  number  accord- 
ing to  the  value  of  the  acceleration  of  gravity  employed  in  the  conversion,  and 
hence  we  find  different  values  in  various  reference  books,  of  which  the  fol- 
lowing may  be  cited: 

Watts. 

Supplee's  Mechanical  Engineer's  Reference  Book  (1904),  page  801 746 

Kent's  Mechanical  Engineers'  Pocketbook: 

(1912),  page  1347 746 

(1913),  page  1347 745-7 

Standard  Handbook  for  Electrical  Engineers  (1908),  page  20,  and  (1910), 

page  21 745. 6 

Foster's  Electrical  Engineer's  Pocketbook  (1908): 

Page  3 : 746 

Page  12 745.  650 

Trautwine's  Civil  Engineers'  Pocketbook  (1909),  page  244 745.  956 

American  Civil  Engineers'  Pocketbook  (1911): 

Page  1197 746 

Page  1313 745.  7 

Bering's  Conversion  Tables  (1904),  page  81 745.  650 

Such  confusion  has  arisen  because  there  has  been  no  accepted  authori- 
tative definition  of  the  horsepower.  When  the  horsepower  is  taken  as  a 
specified  number  of  watts,  it  represents  the  same  amount  of  power  at  all 
places.  But  when  the  horsepower  is  taken  as  a  specified  number  of  foot- 
pounds per  second,  the  amount  of  power  represented  by  it  varies  for  different 
places.  This  is  evident,  since  the  weight  of  a  "pound,"  as  a  unit  of  force, 
varies  in  value  as  g,  the  acceleration  of  gravity,  varies.  Thus,  since  g  is 
greater  for  northern  latitudes  than  for  southern,  the  force  represented  by  a 
definite  number  of  pounds  increases  as  one  goes  north.  This  makes  this 
mode  of  definition  of  the  horsepower  very  unsatisfactory.  It  is  similar  to  a 
proposal  once  made  to  define  the  meter  as  the  length  of  the  seconds  pendu- 
lum. No  one  would  now  consider  seriously  a  unit  of  length  which  varies 
at  different  parts  of  the  earth.  Nevertheless,  units  of  force  having  pre- 

3 


6  Circular  of  the  Bureau  of  Standards 

cisely  that  characteristic  are  in  common  use  at  the  present  time.  The 
gravitational  system  of  units  centers  about  the  gravitational  unit  of  force, 
and  it  is  accordingly  impossible  to  understand  the  subject  without  careful 
consideration  of  the  pound  and  other  gravitational  units  of  force.  For  the 
attainment  of  precise  numerical  relations,  the  value  of  g  must  also  be  care- 
fully considered,  and  authoritative  data  on  this  will  be  given  below. 

H.  THE  POUND  AS  A  UNIT  OF  FORCE 

The  pound  and  the  kilogram  are  primarily  units  of  mass.  It  is  con- 
venient to  use  the  force  of  gravity  upon  masses  to  measure  forces,  so  that 
units  of  the  same  names  are  used  for  force  (or  weight)  as  for  mass.  The 
inherence  of  the  acceleration  of  gravity  in  these  units  of  force  is  often 
forgotten  and  is  the  cause  of  some  confusion.  The  pound  as  a  unit  of  force 
has  generally  been  used  as  a  "gravitational"  unit,  the  characteristic  of  the 
gravitational  units  being  that  their  magnitudes  vary  with  locality  as  g  varies. 
Thus,  a  pound  force  is  equal  to  the  force  of  gravity  on  a  pound  mass  at  any 
place  where  measurements  happen  to  be  made.  The  one  advantage  of  the 
gravitational  system  is  that  a  given  mass  exerts  the  same  number  of  pounds 
of  force  no  matter  what  its  location.  But  by  this  mode  of  definition  the 
magnitude  of  the  pound  force  is  not  constant,  as  it  varies  with  g.  A  few 
writers,  on  the  other  hand,  have  defined  the  pound  force  as  a  fixed  unit, 
taking  it  as  equal  to  the  force  of  gravity  on  a  pound  mass  at  some  one 
particular  place — e.  g.,  Paris,  or  45°  latitude  and  sea  level — thus  destroying 
the  gravitational  character  of  the  unit. 

The  unit  of  force  can  be  made  definite  and  fixed,  however,  without 
abolishing  the  gravitational  system.  This  is  done  by  recognizing  the  dif- 
ference between  the  absolute  and  the  gravitational  pound  by  the  use  of  the 
terms  "standard"  and  "local,"  respectively.  The  principle  involved  is 
that  contained  in  the  definition  of  "standard  weight"  by  the  International 
Conference  on  Weights  and  Measures  in  1901.  The  statement1  by  the 
conference  is  given  herewith: 

The  term  weight  designates  a  quantity  of  the  same  nature  as  a  force;  the  weight  of  a  body 
is  the  product  of  the  mass  of  that  body,  by  the  acceleration  of  gravity;  in  particular,  the  standard 
weight  of  a  body  is  the  product  of  the  mass  of  that  body  by  the  standard  acceleration  of  gravity. 

The  number  adopted  in  the  International  Service  of  Weights  and  Measures  for  the  value  of 
the  standard  acceleration  of  gravity  is  980.665  cm  per  sec.2 

By  analogy  with  "standard  weight,"  the  "standard  pound  force" 
may  be  defined  as  equal  to  the  force  of  gravity  on  a  pound  mass  at  a  place 
where  g  has  the  standard  value,  980.665  cm  per  second  per  second  or  32.1 740 

1  Proces-Verbaux  des  Seances,  Comite  International  des  Poids  et  Mesures,  p.  172;  1901. 


The  Relation  of  the  Horsepower  to  the  Kilowatt  7 

feet  per  second  per  second.  Likewise  the  "  local  pound  force  "  in  any  given 
locality  may  be  defined  as  equal  to  the  force  of  gravity  on  a  pound  mass  in  that 
given  locality.  Similar  definitions  apply  to  the  terms  "  standard  kilogram 
force  "  and  "  local  kilogram  force."  In  specifying  a  force  in  local  units,  it  is 
desirable  to  give  the  location  of  the  place  by  such  expressions,  e.  g.,  as  "  Lon- 
don pounds,"  "  New  York  kilograms,"  "local  kilograms  (0  =  981. 2  6),"  etc. 
The  term  "  standard  "  is  familiar  in  the  sense  here  used,  and  this  application 
of  the  term  "  local  "  was  proposed  to  the  Bureau  by  Prof.  E.  V.  Huntington, 
of  Harvard  University,  in  1913.  To  express  the  force  of  gravity  on  a  mass 
in  standard  pounds,  the  mass  in  pounds  must  be  multiplied  by  the  ratio 
of  the  local  value  of  g  to  980.665. 

The  words  "pound"  and  "kilogram"  used  alone  as  units  of  force  are 
ambiguous.  When  so  used,  the  local  unit  must  usually  be  understood.  This 
has  been  the  usual  sense  of  the  terms  as  used  in  the  past.  Such  an  inter- 
pretation is  clearly  implied  in  the  analogous  statement  on  "weight"  by 
the  international  conference  above.  Writers  who  are  careful  enough  to  use 
standard  pounds  or  kilograms  may  be  expected  to  use  the  word  "  standard  " 
explicitly,  while  those  who  use  the  "pound"  without  thinking  how  it  is 
defined  will  naturally  employ  the  local  unit. 

The  terms  here  given  are  readily  extended  to  derived  units,  based  upon 
the  units  of  force.  Thus,  definitions  follow  at  once  for  "standard  foot- 
pound," "local  foot-pound,"  "standard  kilogram-meter,"  etc. 

m.  THE  VALUE  OF  THE  ACCELERATION  OF  GRAVITY 

The  standard  value  of  g,  980.665  cm  per  second  per  second,  was  origi- 
nally intended  to  represent  the  latitude  of  45°  and  sea  level.  It  has  been 
widely  used  as  a  standard  value  for  barometric  reductions,  etc.,  since  1901, 
and  there  is  no  reason  why  it  should  not  continue  in  use  as  a  standard  value, 
although  the  actual  value  for  45°  and  sea  level  is  now  known  to  be  a  few 
parts  in  100  ooo  different.  The  exact  value  obtained  for  45°  and  sea  level 
varies  with  the  gravity  observations  utilized,  and  also  with  the  theory 
adopted  for  the  "  anomalies,"  or  departures  of  the  observed  values  of  gravity 
for  any  particular  stations  from  the  values  calculated  by  a  general  formula. 
It  is  generally  conceded  to  be  better  to  retain  a  certain  value  as  standard 
rather  than  to  correct  it  from  time  to  time  to  make  it  agree  with  a  theo- 
retical location.  The  value,  980.665,  is  the  result  of  a  calculation  made 
by  the  International  Committee  on  Weights  and  Measures  2  from  Defforges' 
absolute  determination  3  of  g  at  the  International  Bureau  in  1888. 

*  Proces-Verbaux  des  Seances,  p.  165;  1901. 

1  Ibid.,  p.  181,  1891;  Memorial  du  Depot  General  de  la  Guerre,  15,  (i),  1894. 


8  Circular  of  the  Bureau  of  Standards 

In  calculating  the  equivalent  of  the  horsepower  in  various  units  for 
different  latitudes  the  following  formula  is  used : 

£  =  978.038  (i  +0.005302  sin3  <f>  —  0.000007  sin2  2$), 

where  $  is  the  latitude.  This  formula  *  is  accepted  by  the  United  States 
Coast  and  Geodetic  Survey,  and  is  the  result  of  observations  all  over  the 
United  States  with  Hayford's  corrections  for  "isostatic  compensation." 
It  is  referred  to  the  absolute  determination  of  g  at  Potsdam  about  1900. 
(The  Smithsonian  Physical  Tables,  sixth  edition,  1914,  give  this  same 
formula,  except  for  the  use  of  978.030  in  place  of  978.038.  The  value 
978.030  is  based  on  observations  all  over  the  world,  but  neglects  the  iso- 
static corrections.  The  formula  here  given  is  certainly  the  best  available 
for  the  United  States.)  The  theoretical  values  given  by  any  formula  will 
not  in  general  agree  exactly  with  the  actual  values  at  any  particular  place, 
because  of  the  local  "  anomalies  "  caused  by  topography,  etc.  The  depar- 
tures are  in  general  only  a  few  parts  in  100  ooo.  As  this  formula  does  not 
give  g  =  980.665  for  0  =  45°,  the  point  is  once  more  emphasized  that  980.665 
is  an  independent  standard  value,  not  precisely  related  to  a  fixed  locality. 

IV.  PRACTICAL  NEED  FOR  AN  INVARIABLE  UNIT  OF  POWER 

Power  is  very  commonly  measured  with  considerable  precision,  and 
hence  it  is  important  that  the  magnitude  of  the  unit  should  not  vary  from 
place  to  place.  From  the  standpoint  of  metrology  the  definition  of  any 
unit  should  be  rigorous  and  free  from  ambiguity.  The  necessity  for  a 
precise  definition  exists  at  the  present  time  in  engineering  practice.  When 
extensive  research  is  being  made  upon  steam  turbines,  when  tests  are  made 
carefully  and  results  are  interpreted  minutely,  there  should  be  no  uncer- 
tainty in  the  units  used. 

A  precise  definition  is  desirable  even  in  the  commerce  of  to-day.  Misun- 
derstandings might  arise  over  the  acceptance  or  rejection  of  an  engine  under 
test  because  of  the  definition  of  the  unit  of  power.  If  the  power  delivered 
by  the  engine  is  measured  by  the  use  of  a  brake  with  weights,  the  number 
of  foot-pounds  per  second  observed  would  be  greater,  for  example,  at  New 
Orleans  than  at  New  York,  since  the  force  exerted  by  the  weights  is  differ- 
ent for  different  latitudes  and  altitudes.  Consequently,  if  the  horsepower 
is  defined  as  a  definite  number  of  foot-pounds  per  second,  the  same  at  all 
places,  it  is  possible  that  the  engine  might  be  accepted  if  the  test  were  made 

4  Special  Publication  No.  12,  U.  S.  Coast  and  Geodetic  Survey,  p.  10,  1912. 


The  Relation  of  the  Horsepower  to  the  Kilowatt  9 

at  New  Orleans  and  rejected  if  the  test  were  made  at  New  York.  These 
remarks  also  apply  to  the  case  of  testing  an  engine  when  the  force  is  meas- 
ured by  a  dynamometer  or  an  indicator,  as  well  as  when  measured  directly 
by  weights.  If  the  springs  were  all  standardized  at  the  same  place,  then  the 
variation  of  the  force  of  gravity  would  not  enter  the  problem.  However, 
the  elasticity  of  springs  varies  with  temperature,  etc.,  and  hence  in  the 
making  of  an  accurate  test  the  spring  is  calibrated  by  weights  at  the  time 
and  place  of  the  test.  Consequently,  in  any  case  the  variation  of  the  force 
of  gravity  with  locality  must  be  considered  in  interpreting  the  results  of  a 
test.  The  differences  here  discussed  are  less  than  i  per  cent,  and  greater 
errors  than  this  would  be  introduced  in  any  practical  case  by  variation  in 
the  lubrication,  in  the  measurement  of  power,  and  in  the  quality  of  steam. 
Nevertheless,  the  mean  of  a  series  of  tests  would  be  taken  as  the  perform- 
ance of  an  engine,  and  if  this  figure  were  just  on  the  margin  of  tolerance, 
an  uncertain  definition  of  the  horsepower  might  cause  misunderstandings. 
No  such  confusion  is  possible  if  the  horsepower  is  defined  in  such  a  way  as 
to  represent  the  same  amount  of  power  at  all  places. 

On  account  of  the  variation  with  g,  and  because  the  equivalents  of  the 
horsepower  are  not  decimal  multiples  of  any  of  the  fundamental  units,  and, 
further,  because  its  definition  and  value  are  different  on  the  Continent  of 
Europe  from  its  definition  and  value  in  England  and  America,  it  has  long 
been  felt  that  the  horsepower  is  an  unsuitable  unit  for  many  purposes. 
Modern  engineering  practice  is  constantly  tending  away  from  the  horse- 
power and  toward  the  watt  and  kilowatt.  In  Germany  it  has  been  proposed 
to  call  the  kilowatt  "Neupferd"  (new  horsepower),  to  make  its  use  appeal 
more  strongly  to  those  who  have  become  firmly  attached  to  the  horsepower. 
The  objection  to  the  horsepower  has  been  particularly  strong  in  electrical 
engineering.  The  International  Congress  of  Electricians  at  Paris  in  1889 
recommended  that  the  power  of  machines  be  expressed  in  kilowatts  instead 
of  in  horsepower.  A  more  definite  and  powerful  action  with  a  view  to  the 
elimination  of  the  horsepower  was  taken  by  the  International  Electro- 
technical  Commission  at  Turin,  Italy,  in  1911.  This  body,  composed  of 
the  representatives  of  great  electrical  interests  all  over  the  world,  recom- 
mended that  in  all  countries  electrical  machinery,  including  motors,  be 
rated  in  kilowatts  only.  Also,  the  Standards  Committee  of  the  American 
Institute  of  Electrical  Engineers  in  1911  recommended  that  the  kilowatt 
instead  of  the  horsepower  be  used  generally  as  the  unit  of  power. 


I0  Circular  of  the  Bureau  of  Standards 

V.  HISTORICAL 

The  term  "  horsepower  "  as  a  measure  of  the  activity  of  machinery  was 
introduced  5  by  Thomas  Savery,  the  inventor  of  an  early  type  of  steam 
engine.  The  earliest  application  of  the  steam  engine  was  in  the  pumping 
of  water  from  mines,  work  which  had  formerly  been  done  by  horses. 
Savery,  in  his  Miners'  Friend,  page  29,  in  the  year  1 702,  says  that  an  engine 
which  will  raise  as  much  water  as  2  horses  working  continuously  in  a  given 
number  of  hours  will  do  the  work  or  labor  of  about  10  horses,  since  relays 
of  horses  must  be  used  to  keep  the  work  going  continuously ;  such  an  engine, 
then,  he  called  a  lo-horsepower  engine. 

James  Watt,  who  is  generally  known  as  the  inventor  of  the  modern 
steam  engine,  adopted6  the  term  "horsepower"  as  a  unit  for  expressing 
the  power  of  his  steam  engines  and  defined  its  value  in  gravitational  units, 
viz,  foot-pounds  per  minute.  The  magnitude  of  Watt's  horsepower  was, 
however,  six  or  eight  times  as  great  as  Savery's.  The  value  7  was  derived 
from  experiments  made  under  the  direction  of  Watt  and  Boulton,  his 
business  partner,  about  the  year  1775. 

Some  heavy  horses  of  Barclay  &  Perkins's  brewery,  London,  were 
caused  to  raise  a  weight  from  the  bottom  of  a  deep  well  by  pulling  hori- 
zontally on  a  rope  passing  over  a  pulley.  It  was  found  that  a  horse  could 
raise  a  weight  of  100  pounds  while  walking  at  the  rate  of  2.5  miles  per  hour. 
This  is  equivalent  to  22  ooo  foot-pounds  per  minute.  Watt  added  50  per 
cent  to  this  value,  giving  33  ooo  foot-pounds  per  minute,  or  550  foot-pounds 
per  second.  The  addition  of  50  per  cent  was  an  allowance  made  for  friction, 
so  that  a  purchaser  of  one  of  his  engines  might  have  no  ground  for  complaint. 
The  figure  thus  arrived  at  by  Watt  is  admitted  to  be  in  excess  of  the  power 
of  an  average  horse  for  continuous  work,  and  is  probably  at  least  twice  the 
power  of  the  average  horse  working  six  hours  per  day. 

Since  the  time  of  Watt  his  value  has  been  in  general  use  in  England 
and  the  United  States,  and  550  foot-pounds  per  second  is  known  as  the 
English  horsepower.  As  the  use  of  the  steam  engine  spread  from  England 
into  other  countries  the  value  of  the  horsepower  was  translated  into  the 
units  of  the  various  countries;  that  is,  since  the  foot  and  pound  had  different 
values  in  the  different  countries,  the  number  of  foot-pounds  in  a  horsepower 
necessarily  varied.  These  values  were  given  to  the  nearest  round  number, 
and  hence  the  equivalence  to  the  English  horsepower  was  only  approximate, 
the  value  averaging  about  i  per  cent  smaller.  Hence  arose  the  discrepancies 
shown  in  Table  i . 

6  The  Life  of  James  Watt,  by  J.  P.  Muirhead  (London,  1858),  p.  153. 

ejohn  Robinson,  Mechanical  Philosophy,  Vol.  II  (Edinburgh,  1822). 

7 1.  P.  Church,  Statics  and  Dynamics  (New  York,  1886),  p.  136.  Encyclopedia  Britannica,  4th  edition,  article  on 
"Steam  and  steam  engines,"  written  by  John  Robison,  with  footnotes  by  James  Watt,  jr.  T.  W.  Wright,  Elements  of 
Mechanics  (New  York,  1896),  p.  251. 


The  Relation  of  the  Horsepower  to  the  Kilowatt 

TABLE  1 
Various  Values  Adopted  For  The  Horsepower 

[Foot-Pounds  Given  in  Terms  of  the  Local  Foot  and  Pound] 


II 


Foot- 
pounds per 
second 

English 
horse- 
power 

Kilogram- 
meters  per 
second 

Authority  » 

England  and  United  States 

550 

1  0000 

76  041 

\ 

Austria  (old)  

430. 

1.0010 

76.  119 

H 

Switzerland  

500. 

0  9863 

75  000 

A 

600 

0  9856 

74  943 

N 

Russia  

550. 

1.0000 

76.041 

N 

Prussia.. 

480 

0  9906 

75  325 

H 

530 

0  9869 

75  045 

H 

Baden  

500. 

0  9863 

75  000 

H 

525 

0  9890 

75  204 

H 

Bavaria  

460. 

0.9888 

75.  190 

K 

Austria 

France  

>  

0.9863 

75.000 

V 

Italy,  etc 

8  v=various.  H=Des  Ingenieurs  Taschenbuch-Hutte  II  (Berlin,  1902).  A=F.  Autenheimer,  Mechanische  Arbeit 
(Stuttgart,  1871),  p.  15.  N=J.  W.  Nystrom,  Elements  of  Mechanics  (Philadelphia,  1873),  p.  63.  K=KarmarsCh  und 
Heeren's  Technisches  Worterbuch  VI  (1883),  p.  637;  and  Alexander's  Weights  and  Measures  (Baltimore,  1850). 

After  the  metric  system  had  come  into  use  in  France,  Germany,  and 
Austria  the  values  of  the  horsepower  in  the  various  countries  were  reduced 
to  kilogram-meters  per  second,  with  the  results  shown  in  the  table.  The 
values  range  from  75  to  76  kilogram-meters  per  second,  averaging  only  a 
little  more  than  75.  Hence,  this  round  value,  75,  has  been  adopted  gen- 
erally on  the 'Continent  as  the  value  of  the  horsepower. 

The  English  value,  550  foot-pounds  per  second,  is,  however,  equivalent 
to  76.041  kilogram-meters  per  second,  and  hence  it  is  that  there  is  a  difference 
of  nearly  1.5  per  cent  between  the  value  generally  used  in  English  and 
American  practice  and  that  used  in  continental  practice.  Reduced  to  watts, 
the  English  horsepower  is  generally  taken  as  746  watts,  although  the  precise 
equivalent,  in  watts,  of  550  foot-pounds  per  second  depends  on  the  accelera- 
tion of  gravity,  and  hence  on  the  latitude  and  altitude.  This  is  discussed 
fully  below. 

It  is  unfortunate  that  the  value  of  the  horsepower  on  the  Continent 
of  Europe  was  not  taken  as  76  kilogram-meters  per  second  instead  of  75, 
in  order  that  it  might  agree  with  the  English  value,  as  was  originally  in- 
tended. It  is  perhaps  unlikely  that  a  change  to  76  could  now  be  made, 
or  that  an  agreement  could  be  reached  by  which  the  continental  and  the 


12  Circular  of  the  Bureau  of  Standards 

English  horsepower  would  correspond  to  the  same  number  of  watts.  It  is  to 
some  extent  customary  for  continental  writers  to  distinguish  the  two  horse- 
powers by  the  words  "English"  and  "metric."  We  shall  call  the  latter 
the  "continental  horsepower."  Thus,  German  writers  speak  of  the  "Eng- 
lische  Pf  erdestarke  "  and  the  "metrische  Pf  erdestarke. "  The  term  "  Pf  er- 
destarke "  is  now  the  preferred  name  for  the  horsepower  in  Germany,  the 
old  term  " Pf erdekraf t "  being  unsuitable  because  "Kraft"  means  "force." 
Similarly,  in  France,  the  old  term  "  force-de-cheval "  has  been  given  up  for 
"cheval-vapeur."  There  is  another  unit  of  power  which  has  been  used  in 
Europe,  the  "poncelet,"  or  100  kilogram-meters  per  second.  This  unit 
was  named  in  honor  of  Jean  Victor  Poncelet,  who  introduced  the  teaching 
of  kinematics  at  the  Sorbonne  in  1838.  This  unit  was  adopted  in  France 
shortly  before  1846,  according  to  C.  F.  Peschel.9  It  was  adopted  as  a  unit 
of  power  in  1889  by  the  "Congres  international  de  mecanique  appliquee." 
Its  use  is  still  permitted  in  the  electrical  regulations  issued  by  the  "Associa- 
tion alsacienne  des  Proprietaires  d'Appareils  a  Vapeur."  It  has  not,  how- 
ever, been  much  used  in  practice.10  This  is  probably  due  in  part  to  the 
fact  that  the  horsepower  had  so  firm  a  hold  as  the  unit  of  power,  and  in  part 
to  the  very  near  equivalence  of  the  poncelet  to  the  kilowatt.  The  poncelet 
is  open  to  the  same  objection  as  the  horsepower  when  the  latter  is  rigidly 
defined  as  a  certain  number  of  foot-pounds  or  kilogram-meters  per  second, 
viz,  that  the  power  it  represents  varies  from  place  to  place. 

VI.  EQUIVALENTS  OF  THE  ENGLISH  AND  AMERICAN  HORSEPOWER 

It  is  possible  to  define  the  horsepower  in  such  a  way  that  the  value 
determined  by  James  Watt  will  be  continued  and  yet  the  unit  will  repre- 
sent the  same  rate  of  -work  at  all  places.  The  convenient  and  frequently 
used  equivalent,  746  watts,  happens  to  be  equal  to  the  rate  of  work  ex- 
pressed by  550  local  foot-pounds  per  second  at  50°  latitude  and  sea  level, 
nearly  the  latitude  of  London,  where  Watt's  original  experiments  to  deter- 
mine the  horsepower  were  made.  The  horsepower  is  therefore  taken  to  be 
equal  to  the  definite  amount  of  power,  746  watts,  and  in  consequence  the 
number  of  foot-pounds  per  second  corresponding  to  i  horsepower  varies 
with  the  value  of  g.  The  number  of  standard  "  foot-pounds  per  second  in  a 
horsepower  =  5 50.22.  The  same  rate  of  work  is  expressed  by  a  larger 
number  of  foot-pounds  per  second  in  lower  latitudes  and  higher  altitudes, 

'  Peschel's  Elements  of  Physics,  Vol.  II,  p.  250  (London,  1846). 
M  Olof  Linders,  Physikalischen  Grossen. 
11  As  explained  in  Sec.  II,  the  standard  foot-pound  is  that  corresponding  to  9=980.665. 


The  Relation  of  the  Horsepower  to  the  Kilowatt 


where  the  force  of  gravity  is  less,  and  by  a  smaller  number  of  foot-pounds 
per  second  in  higher  latitudes  where  the  force  of  gravity  is  greater.  Table  2 
gives  the  number  of  foot-pounds  per  second  in  a  horsepower  at  various 
latitudes  and  altitudes.  The  value  of  g  at  sea  level  is  obtained  from  the 
formula  given  in  Section  III.  The  change  with  altitude  is  calculated  from 
the  correction  to  the  value  of  g,  viz,  —0.000192  per  meter  elevation. 
The  number  given  in  the  table  for  45°  and  sea  level  is  550.24;  the  fact 
that  it  differs  from  the  number  of  "standard"  foot-pounds  per  second, 
above,  emphasizes  again  the  fact  that  the  standard  value  of  g  does  not  corre- 
spond quite  exactly  to  45°  and  sea  level. 

TABLE  2 

Value  of  the  English  and  American  Horsepower  (746  Watts)  in  Local  Foot-Pounds 
per  Second  at  Various  Latitudes  and  Altitudes 


Latitude 

Altitude 

0° 
(equator) 

30° 

45° 

60° 

90" 
(pole) 

Sea  level 

551  70 

550  97 

550  24 

549  52 

548  79 

SOOOIeet  

551.  86 

551.  13 

550.  41 

549.68 

548.95 

10000  feet 

552.03 

551.30 

550.57 

549  85 

549  12 

The  foregoing  table  may  be  put  in  the  following  approximate  form 
for  ease  of  remembering: 

TABLE  3 

English  and  American  Horsepower  (746  Watts)  at  Various  Latitudes 


Local  foot- 
pounds ] 


(approx.) 


90°,  pole 

50°,  London 

(39°,  Washington) 

30°,  New  Orleans 

0°,  equator 


549 
550 

(550.5) 
551 
552 


The  value  of  the  English  horsepower  may  also  be  given  in  metric  units 
for  various  latitudes  and  altitudes,  as  follows: 


14  Circular  of  the  Bureau  of  Standards 

TABLE  4 

Value  ofvthe  English  and  American  Horsepower  (746  Watts)  in  Local  Kilogram- 
Meters  per  Second  at  Various  Latitudes  and  Altitudes 


Latitude 

Altitude 

0° 
(equator) 

30° 

45° 

60° 

90° 
(pole) 

76  275 

76  175 

76  074 

75  973 

75  873 

1500  meters  (-5000  feet  approximately)  

76.297 

76.  197 

76.096 

75.995 

75.895 

3000  meters  (—  10000  feet  approximately) 

76  320 

76  220 

76  119 

76  018 

75.  918 

By  interpolation  one  can  take  out  of  these  tables  the  proper  value  of 
the  horsepower  in  gravitation  measure  (either  foot-pounds  or  kilogram- 
meters  per  second)  for  any  latitude  and  altitude. 

VEL  EQUIVALENTS  OF  THE  CONTINENTAL  HORSEPOWER 

The  continental  horsepower  is  generally  given  either  as  75  kilogram- 
meters  per  second  or  as  736  watts.  These  two  equivalents  are  independent 
definitions  and  are  likely  to  cause  confusion  unless  one  of  them  is  assigned 
to  some  definite  place  on  the  earth's  surface.  As  pointed  out  in  the  pre- 
ceding sections  of  this  circular,  the  unit,  to  be  definite,  should  represent 
the  same  rate  of  work  at  all  places.  The  continental  horsepower,  then, 
should  be  taken  as  736  watts,  which  is  equivalent  to  75  local  kilogram- 
meters  per  second  at  latitude  52°  30',  or  Berlin.  The  number  of  kilogram- 
meters  per  second  expressing  this  amount  of  power  will  be  smaller  than  75 
at  more  northern  latitudes  and  larger  at  lower  latitudes.  The  values  at 
various  latitudes  at  sea  level  are  given  in  Table  5: 

TABLE  5 
Continental  Horsepower  (736  Watts)  in  Local  Kilogram-Meters  per  Second 


Altitude 

0° 
(equator) 

30° 

45° 

60" 

90" 
(pole) 

Sea  level                                                                           

75.253 

75.153 

75.054 

74.  955 

74.856 

1500  meters 

75  275 

75  175 

75  076 

74  977 

74  878 

3000  meters        

75.297 

75.  197 

75.098 

74.999 

74.900 

The  Relation  of  the  Horsepower  to  the  Kilowatt  15 

vm.  CONCLUSIONS 

It  is  considered  desirable  that  the  watt  and  kilowatt  be  used  as  the 
units  of  power,  whenever  possible,  for  all  kinds  of  scientific,  engineering,  and 
other  work.  It  is  not  unlikely  that  the  unit  of  horsepower  will  ultimately 
go  out  of  use.  In  the  meantime,  however,  it  is  desirable  that  its  definition 
be  uniform.  This  circular  has  been  written  to  point  out  that  if  the  horse- 
power is  to  represent  the  same  amount  of  power  at  different  places  its  relation 
to  the  watt  must  be  a  constant  number,  and  the  number  of  local  foot- 
pounds or  kilogram-meters  per  second  which  it  represents  must  vary  from 
place  to  place.  Table  2  and  others  of  this  circular  show  clearly  this  varia- 
tion with  locality. 

It  might  be  feared  that  some  confusion  could  arise  because  of  the  inde- 
pendent definitions  of  the  mechanical  watt  and  the  "international"  elec- 
trical watt.  The  watt  and  kilowatt  are  defined  primarily  in  purely  mechan- 
ical terms,  and  not  electrically  at  all.  That  they  have  been  used  mainly 
in  electrotechnical  work  is  merely  accidental  and  is  due  to  the  fact  that 
they  are  metric  units  and  so  fit  in  naturally  with  the  metric  units  in  which 
all  electrical  quantities  are  universally  expressed.  Any  kind  of  power  may 
properly  be  measured  in  kilowatts.  For  example,  in  the  case  of  the  hydraulic 
power  furnished  by  a  flowing  stream,  the  total  power  is  given  in  kilowatts 
by  multiplying  0.163  into  the  product  of  the  head  in  meters  by  the  flow  in 
cubic  meters  per  minute ;  the  total  power  is  likewise  given  in  kilowatts  by 
multiplying  0.00141  into  the  product  of  the  head  in  feet  by  the  flow  in  cubic 
feet  per  minute.  The  watt  is  defined  directly  in  terms  of  the  fundamental 
units  of  mass,  length,  and  time,  in  the  "meter-kilogram-second"  system,  thus : 
"The  watt  is  the  power  developed  by  the  action,  with  a  velocity  of  i  meter 
per  second,  of  a  force  capable  of  giving  to  a  mass  of  i  kilogram  in  one  second 
a  velocity  of  i  meter  per  second."  The  "international  watt,"  however,  is 
defined  in  terms  of  concrete  electrical  standards,  which  electrical  standards 
represent  practically,  as  nearly  as  the  limitations  of  experiment  allow,  the 
absolute  electrical  quantities  in  terms  of  their  theoretical  relations  to  length, 
mass,  and  time.  The  international  watt  thus  defined  is  the  closest  concrete 
realization  of  the  theoretical  absolute  or  mechanical  watt  which  we  have. 
Measurements  have  indicated  that  the  international  watt  is  not  more  than 
3  parts  in  10  ooo  greater  than  the  absolute  watt.  Consequently,  there  is 
in  reality  no  confusion  between  the  mechanical  watt  and  the  international 
electrical  watt. 


1 6  Circular  of  the  Bureau  of  Standards 

It  is  recommended  that  engineering  societies  and  other  interests  con- 
cerned recognize  the  value  of  the  "English  and  American  horsepower"  as 
746  watts  (or  550  foot-pounds  per  second  at  50°  latitude  and  sea  level, 
approximately  the  latitude  of  London),  employing  Table  2  to  obtain  the 
value  in  foot-pounds  per  second  at  other  places.  It  is  likewise  recom- 
mended that  the  value  of  the  "continental  horsepower"  be  taken  uniformly 
as  736  watts  (or  75  kilogram-meters  per  second  at  latitude  52°  30',  the  lati- 
tude of  Berlin),  and  that  the  value  in  kilogram-meters  per  second  at  other 
places  be  obtained  from  such  a  table  as  Table  5  of  this  circular. 

These  values  were  adopted  by  a  committee  of  the  British  Association 
for  the  Advancement  of  Science  in  1873.  This  was  the  committee  which 
recommended  the  cgs  system,  and  on  it  were  Sir  W.  Thomson,  Carey  Fos- 
ter, Clerk  Maxwell,  J.  D.  Everett,  and  others  (B.  A.  Report  1873,  P-  222). 
The  committee  in  its  report  said:  "One  horsepower  is  about  three-fourths 
of  an  erg-ten  per  second.  More  nearly,  it  is  7.46  erg-nines  per  second;  and 
one  force-de-cheval  is  7.36  erg-nines  per  second."  (One  erg-nine=  100 
watts.) 

The  Standards  Committee  of  the  American  Institute  of  Electrical 
Engineers  adopted,  on  May  16,  1911,  the  following  rule,  which  was  inserted 
in  the  Standardization  Rules  of  the  Institute: 

In  view  of  the  fact  that  a  horsepower  defined  as  550  foot-pounds  per  second  represents  a  power 
which  varies  slightly  with  the  latitude  and  altitude  (from  743.3  to  747.6  watts),  and  also  in  view  of 
the  fact  that  different  authorities  differ  as  to  the  precise  value  of  the  horsepower  in  watts,  the 
standards  committee  has  adopted  746  watts  as  the  value  of  the  horsepower.  The  number 
of  foot-pounds  per  second  to  be  taken  as  i  horsepower  is  therefore  such  a  value  at  any  given 
place  as  is  equivalent  to  746  watts;  the  number  varies  from  552  to  549  foot-pounds  per  second, 
being  550  at  50°  latitude  (London),  and  550.5  at  Washington.  The  Standards  Committee,  how- 
ever, recommends  that  the  kilowatt  instead  of  the  horsepower  be  used  generally  as  the  unit  of 
power. 

The  same  value,  746  watts,  is  used  by  the  Bureau  of  Standards  as  the 
exact  equivalent  of  the  English  and  American  horsepower.  The  Bureau 
recommends  the  use,  whenever  possible,  of  the  kilowatt  instead  of  the 
horsepower. 


QC 
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t/58r 
1915 


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